(a) A man travels from a village X on a bearing of 060° to a village Y which is 20km away. From Y, he travels to a village Z, on a bearing of 195°. If Z is directly east of X, calculate, correct to three significant figures, the distance of : (i) Y from Z ; (ii) Z from X . (b) An aircraft flies due South from an airfield on latitude 36°N, longitude 138°E to an airfield on latitude 36°S, longitude 138°E. (i) Calculate the distance travelled, correct to three significant figures ; (ii) if the speed of the aircraft is 800km per hour, calculate the time taken, correct to the nearest hour. [Take , R = 6400km].
Explanation
(a) < XZY = 180° - (30° + 45°) = 105°
(to 3 sig. figs) (ii) ( to 3 sig. figs) (b) Let P and Q be two airfields.
Difference in latitude = 36° + 36° = 72° (i) Distance between P and Q = = = (3 sig. figs) (ii) Time taken = (to the nearest hour)
